Analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

Analytical Approximations to Predict Performance Measures of Manufacturing Systems with Job Failures and Parallel Processing

Parallel processing is prevalent in many manufacturing and service systems. Many manufactured products are built and assembled from several components fabricated in parallel lines. An example of this manufacturing system configuration is observed at a manufacturing facility equipped to assemble and test web servers. Characteristics of a typical web server assembly line are: multiple products, job circulation, and paralleling processing. The primary objective of this research was to develop analytical approximations to predict performance measures of manufacturing systems with job failures and parallel processing. The analytical formulations extend previous queueing models used in assembly manufacturing systems in that they can handle serial and different configurations of paralleling processing with multiple product classes, and job circulation due to random part failures. In addition, appropriate correction terms via regression analysis were added to the approximations in order to minimize the gap in the error between the analytical approximation and the simulation models. Markovian and general type manufacturing systems, with multiple product classes, job circulation due to failures, and fork and join systems to model parallel processing were studied. In the Markovian and general case, the approximations without correction terms performed quite well for one and two product problem instances. However, it was observed that the flow time error increased as the number of products and net traffic intensity increased. Therefore, correction terms for single and fork-join stations were developed via regression analysis to deal with more than two products. The numerical comparisons showed that the approximations perform remarkably well when the corrections factors were used in the approximations. In general, the average flow time error was reduced from 38.19% to 5.59% in the Markovian case, and from 26.39% to 7.23% in the general case. All the equations stated in the analytical formulations were implemented as a set of Matlab scripts. By using this set, operations managers of web server assembly lines, manufacturing or other service systems with similar characteristics can estimate different system performance measures, and make judicious decisions - especially setting delivery due dates, capacity planning, and bottleneck mitigation, among others.

Closed form approximations for spread options

This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option and a corresponding approximation for each of its price, volatility and correlation hedge ratios. Our approach has many advantages over existing analytical approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur costs. Simulations quantify the accuracy of our approach; we also present an empirical application to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996, Correlation in energy markets. In: V. Kaminski (Ed.), Managing Energy Price Risk, pp. 71–78 (London: Risk Publications)), which is commonly used by traders.

Approximations for the generalized temperature integral: a method based on quadrature rules

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

Green-Ampt approximations

The solution to the Green and Ampt infiltration equation is expressible in terms of the Lambert W-1 function. Approximations for Green and Ampt infiltration are thus derivable from approximations for the W-1 function and vice versa. An infinite family of asymptotic expansions to W-1 is presented. Although these expansions do not converge near the branch point of the W function (corresponds to Green-Ampt infiltration with immediate ponding), a method is presented for approximating W-1 that is exact at the branch point and asymptotically, with interpolation between these limits. Some existing and several new simple and compact yet robust approximations applicable to Green-Ampt infiltration and flux are presented, the most accurate of which has a maximum relative error of 5 x 10(-5)%. This error is orders of magnitude lower than any existing analytical approximations. (c) 2005 Elsevier Ltd. All rights reserved.

Electromagnetic Wave Scattering by Schwarzschild Black Holes

We analyze the scattering of a planar monochromatic electromagnetic wave incident upon a Schwarzschild black hole. We obtain accurate numerical results from the partial wave method for the electromagnetic scattering cross section and show that they are in excellent agreement with analytical approximations. The scattering of electromagnetic waves is compared with the scattering of scalar, spinor, and gravitational waves. We present a unified picture of the scattering of all massless fields for the first time.

How cracks in SiOx-coated polyester films affect gas permeation

In this paper theoretical models have been established that can account for the gas transmission through nanocomposite laminates, consisting of an oxide layer of finite permeability containing defects, on a polymer sheet of finite thickness. The defect shapes can either be in the form of long cracks or rectangular holes. The models offer a choice of exact numerical calculations or fast and intuitive analytical approximations. The experimental measurements of oxygen permeation through four different SiOx/poly (ethylene terephthalate) samples that were strained to produce distributions or cracks showed good agreement when compared with predicted results from the approximate analytic model. As a consequence of this observation, a key practical conclusion is that, because of the logarithmic dependence of transmission on the width of a crack, for a given strain it is better to have a small number of large cracks rather than a large number of small cracks. (C) 2001 Elsevier Science B.V. All rights reserved.

Approximation de la distribution a posteriori d'un modèle Gamma-Poisson hiérarchique à effets mixtes

La méthode que nous présentons pour modéliser des données dites de "comptage" ou données de Poisson est basée sur la procédure nommée Modélisation multi-niveau et interactive de la régression de Poisson (PRIMM) développée par Christiansen et Morris (1997). Dans la méthode PRIMM, la régression de Poisson ne comprend que des effets fixes tandis que notre modèle intègre en plus des effets aléatoires. De même que Christiansen et Morris (1997), le modèle étudié consiste à faire de l'inférence basée sur des approximations analytiques des distributions a posteriori des paramètres, évitant ainsi d'utiliser des méthodes computationnelles comme les méthodes de Monte Carlo par chaînes de Markov (MCMC). Les approximations sont basées sur la méthode de Laplace et la théorie asymptotique liée à l'approximation normale pour les lois a posteriori. L'estimation des paramètres de la régression de Poisson est faite par la maximisation de leur densité a posteriori via l'algorithme de Newton-Raphson. Cette étude détermine également les deux premiers moments a posteriori des paramètres de la loi de Poisson dont la distribution a posteriori de chacun d'eux est approximativement une loi gamma. Des applications sur deux exemples de données ont permis de vérifier que ce modèle peut être considéré dans une certaine mesure comme une généralisation de la méthode PRIMM. En effet, le modèle s'applique aussi bien aux données de Poisson non stratifiées qu'aux données stratifiées; et dans ce dernier cas, il comporte non seulement des effets fixes mais aussi des effets aléatoires liés aux strates. Enfin, le modèle est appliqué aux données relatives à plusieurs types d'effets indésirables observés chez les participants d'un essai clinique impliquant un vaccin quadrivalent contre la rougeole, les oreillons, la rub\'eole et la varicelle. La régression de Poisson comprend l'effet fixe correspondant à la variable traitement/contrôle, ainsi que des effets aléatoires liés aux systèmes biologiques du corps humain auxquels sont attribués les effets indésirables considérés.

Latitude and longitude vertical disparities

The literature on vertical disparity is complicated by the fact that several different definitions of the term “vertical disparity” are in common use, often without a clear statement about which is intended or a widespread appreciation of the properties of the different definitions. Here, we examine two definitions of retinal vertical disparity: elevation-latitude and elevation-longitude disparities. Near the fixation point, these definitions become equivalent, but in general, they have quite different dependences on object distance and binocular eye posture, which have not previously been spelt out. We present analytical approximations for each type of vertical disparity, valid for more general conditions than previous derivations in the literature: we do not restrict ourselves to objects near the fixation point or near the plane of regard, and we allow for non-zero torsion, cyclovergence, and vertical misalignments of the eyes. We use these expressions to derive estimates of the latitude and longitude vertical disparities expected at each point in the visual field, averaged over all natural viewing. Finally, we present analytical expressions showing how binocular eye position—gaze direction, convergence, torsion, cyclovergence, and vertical misalignment—can be derived from the vertical disparity field and its derivatives at the fovea.

Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV

This paper presents the mathematical development of a body-centric nonlinear dynamic model of a quadrotor UAV that is suitable for the development of biologically inspired navigation strategies. Analytical approximations are used to find an initial guess of the parameters of the nonlinear model, then parameter estimation methods are used to refine the model parameters using the data obtained from onboard sensors during flight. Due to the unstable nature of the quadrotor model, the identification process is performed with the system in closed-loop control of attitude angles. The obtained model parameters are validated using real unseen experimental data. Based on the identified model, a Linear-Quadratic (LQ) optimal tracker is designed to stabilize the quadrotor and facilitate its translational control by tracking body accelerations. The LQ tracker is tested on an experimental quadrotor UAV and the obtained results are a further means to validate the quality of the estimated model. The unique formulation of the control problem in the body frame makes the controller better suited for bio-inspired navigation and guidance strategies than conventional attitude or position based control systems that can be found in the existing literature.

K-41(n, gamma)K-42 thermal and resonance integral cross section measurements

We measured the K-41 thermal neutron absorption and resonance integral cross sections after the irradiation of KNO3 samples near the core of the IEA-R1 IPEN pool-type research reactor. Bare and cadmium-covered targets were irradiated in pairs with Au-Al alloy flux-monitors. The residual activities were measured by gamma-ray spectroscopy with a HPGe detector, with special care to avoid the K-42 decay beta(-) emission effects on the spectra. The gamma-ray self-absorption was corrected with the help of MCNP simulations. We applied the Westcott formalism in the average neutron flux determination and calculated the depression coefficients for thermal and epithermal neutrons due to the sample thickness with analytical approximations. We obtained 1.57(4) and 1.02(4) b, for thermal and resonance integral cross sections, respectively, with correlation coefficient equal to 0.39.

Incorporação do espalhamento Compton no modelo de TBC modificado

No último século, houve grande avanço no entendimento das interações das radiações com a matéria. Essa compreensão se faz necessária para diversas aplicações, entre elas o uso de raios X no diagnóstico por imagens. Neste caso, imagens são formadas pelo contraste resultante da diferença na atenuação dos raios X pelos diferentes tecidos do corpo. Entretanto, algumas das interações dos raios X com a matéria podem levar à redução da qualidade destas imagens, como é o caso dos fenômenos de espalhamento. Muitas abordagens foram propostas para estimar a distribuição espectral de fótons espalhados por uma barreira, ou seja, como no caso de um feixe de campo largo, ao atingir um plano detector, tais como modelos que utilizam métodos de Monte Carlo e modelos que utilizam aproximações analíticas. Supondo-se um espectro de um feixe primário que não interage com nenhum objeto após sua emissão pelo tubo de raios X, este espectro é, essencialmente representado pelos modelos propostos anteriormente. Contudo, considerando-se um feixe largo de radiação X, interagindo com um objeto, a radiação a ser detectada por um espectrômetro, passa a ser composta pelo feixe primário, atenuado pelo material adicionado, e uma fração de radiação espalhada. A soma destas duas contribuições passa a compor o feixe resultante. Esta soma do feixe primário atenuado, com o feixe de radiação espalhada, é o que se mede em um detector real na condição de feixe largo. O modelo proposto neste trabalho visa calcular o espectro de um tubo de raios X, em situação de feixe largo, o mais fidedigno possível ao que se medem em condições reais. Neste trabalho se propõe a discretização do volume de interação em pequenos elementos de volume, nos quais se calcula o espalhamento Compton, fazendo uso de um espectro de fótons gerado pelo Modelo de TBC, a equação de Klein-Nishina e considerações geométricas. Por fim, o espectro de fótons espalhados em cada elemento de volume é somado ao espalhamento dos demais elementos de volume, resultando no espectro total espalhado. O modelo proposto foi implementado em ambiente computacional MATLAB® e comparado com medições experimentais para sua validação. O modelo proposto foi capaz de produzir espectros espalhados em diferentes condições, apresentando boa conformidade com os valores medidos, tanto em termos quantitativos, nas quais a diferença entre kerma no ar calculado e kerma no ar medido é menor que 10%, quanto qualitativos, com fatores de mérito superiores a 90%.

Massive MIMO in sparse channels

Massive multi-user multiple-input multiple-output (MU-MIMO) systems are cellular networks where the base stations (BSs) are equipped with hundreds of antennas, N, and communicate with tens of mobile stations (MSs), K, such that, N ≫ K ≫ 1. Contrary to most prior works, in this paper, we consider the uplink of a single-cell massive MIMO system operating in sparse channels with limited scattering. This case is of particular importance in most propagation scenarios, where the prevalent Rayleigh fading assumption becomes idealistic. We derive analytical approximations for the achievable rates of maximum-ratio combining (MRC) and zero-forcing (ZF) receivers. Furthermore, we study the asymptotic behavior of the achievable rates for both MRC and ZF receivers, when N and K go to infinity under the condition that N/K → c ≥ 1. Our results indicate that the achievable rate of MRC receivers reaches an asymptotic saturation limit, whereas the achievable rate of ZF receivers grows logarithmically with the number of MSs.

Alternative Analytical Expressions for the General van Genuchten-Mualem and van Genuchten-Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properties, first published in 1980, are used frequently in various vadose zone flow and transport applications assuming a specific relationship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conductivity equations, the more general solutions with independent m and n values are rarely used. We expressed the general van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity equations in terms of hypergeometric functions, which can be approximated by infinite series that converge rapidly for relatively large values of the van Genuchten-Mualem parameter n but only very slowly when n is close to one. Alternative equations were derived that provide very close approximations of the analytical results. The newly proposed equations allow the use of independent values of the parameters m and n in the soil water retention model of van Genuchten for subsequent prediction of the van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity models, thus providing more flexibility in fitting experimental pressure-head-dependent water content, theta(h), and hydraulic conductivity, K(h), or K(theta) data.